In order to understand the phenomenological
implications of this model dependence, we briefly recall here the argument of
Refs. [1]}, [2]} regarding the energy-enhanced emission of the longitudinal modes of \(\mathcal {X}\) 
stemming from the WZ operators.
Taking the limit \(g_{X}\rightarrow 0\)  and \(m_{\mathcal {X}}\rightarrow 0\) ,
while keeping fixed the ratio \(m_{\mathcal {X}} / g_{X} \propto v_X\) ,
the transverse modes of \(\mathcal {X}\)  decouple,
while the longitudinal mode is enhanced as \(E / m_{\mathcal {X}}\) .
In this regime, the equivalence theorem states that the longitudinally polarized vectors are equivalent
to the corresponding scalar Goldstone bosons.
This is readily seen by working in the
so-called “Equivalent Gauge” of Ref. [3]},
where the longitudinally polarized state, \(|\mathcal {X}_{L}\rangle \) , is represented as
\(\langle 0|\mathcal {X}_{\mu }(x)|\mathcal {X}_{L}(\vec{p})\rangle =\epsilon _{\mu }^{L}(\vec{p})e^{-ipx} \, ,\qquad \langle 0|\xi (x)|\mathcal {X}_{L}(\vec{p})\rangle =-ie^{-ipx} \, ,\) 
